Wound angiogenesis as a function of tissue oxygen tension: A mathematical model

Abstract

therapeutics ͉ redox ͉ translational research ͉ hypoxia ͉ hyperoxia

A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies

“…Most of the modeling studies on wound healing consider only one partial process. The papers on continuum hypothesis-based models for wound healing can be classified into -models for contraction, for instance the work by Olsen et al (1995), Murray (2004), Vermolen (2009), where both mechanistic effects from pulling forces exerted by (myo-)fibroblasts, proliferation, cell mobility and chemical interactions are dealt with; -models for wound angiogenesis, in which we mention, among many others, the studies carried out by Maggelakis (2004), Schugart et al (2008), Xue et al (2009), andGaffney (2002). In some of these studies, the shortage of oxygen is taken into account as a trigger for angiogenesis.…”

A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell–cell contacts

“…These models are useful on a tissue scale, where cells are not tracked, but rather cell densities are modeled. Some of these PDE models track the interface between for instance wound or tumor and the undamaged tissue, explicitly by incorporating a moving boundary problem (Adam 1999;Mi et al 2007;Arciero et al 2011;Schugart et al 2008;Xue et al 2009;Javierre et al 2008;Vermolen and Javierre 2009). Further, (Armstrong et al 2006;Gerisch and Chaplain 2006), some studies were performed based on the use of non-local (integral) terms in PDE's to simulate interfaces between different cell-types.…”

A finite-element model for healing of cutaneous wounds combining contraction, angiogenesis and closure

“…Here, we also mention some continuum models for angiogenesis, which is an essential process within wound healing. Some studies were done by Schugart et al (2008), Maggelakis (2004) and Gaffney et al (2002), to mention a few. The model due to Schugart et al (2008) sets up a complete picture for dermal wound healing in the sense that the fibroblasts, extracellular matrix, inflammatory cells, capillary sprouts and tips are taken into account.…”

“…This is also done in studies on tumor growth, as in Hogea et al (2006), where the level set method is used to track the tumor boundary. In Schugart et al (2008), Xue et al (2009), Vermolen and Adam (2007), Javierre et al (2008), Vermolen (2009), Vermolen andJavierre (2009b, 2010), several attempts were made to combine these partial processes to get a more complete model for dermal wound healing. In Schugart et al (2008) and Xue et al (2009), the models focused on angiogenesis and dermal regeneration, but visco-elastic effects were left out.…”

“…In Schugart et al (2008), Xue et al (2009), Vermolen and Adam (2007), Javierre et al (2008), Vermolen (2009), Vermolen andJavierre (2009b, 2010), several attempts were made to combine these partial processes to get a more complete model for dermal wound healing. In Schugart et al (2008) and Xue et al (2009), the models focused on angiogenesis and dermal regeneration, but visco-elastic effects were left out. Whereas, in Vermolen and Adam (2007) and Vermolen (2009), it was focused on a combination of angiogenesis and reepithelialization (closure of the epidermis).…”